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ExampleConstruction: AI-generatedVerification: AI-adaptedPipeline-generatedprecheck passjudge pass (gpt-6-luna)
How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

A deterministic Dörfler mark on three cells

Example

Take squared cell indicators (9,4,1) in the stated identifier order and θE=3/5.

Facts & Assumptions

Given: Three nonnegative squared indicators and the deterministic prefix rule of Dorfler marking and conforming newest-vertex refinement.

[F1]

Dörfler marking selects the shortest descending-value prefix whose sum reaches the declared fraction of the total (Dorfler marking and conforming newest-vertex refinement).

Verification

1.1F1givenalgebra

The total is 9+4+1=14, so the threshold is (3/5)14=42/5=8.4. The sorted descending prefix sums are 9,13,14.

2.1step 1.1algebra∎

The first prefix already has sum 9≥8.4, while the empty prefix has sum 0<8.4. Thus the unique minimal mark is the first cell, regardless of the later tie rule.

Finite check

The three prefixes are exactly ∅, {1}, {1,2} and {1,2,3} with sums 0,9,13,14; the first threshold-crossing prefix has cardinality one.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources